Ordinary people could expect to meet a saint though it would not be an everyday thing. More commonly, they could expect to meet a saint soon after that “saint’s” death. Sainthood was more an ascribed than an achieved attribute through most of the Middle Ages. Anyone who died an untimely, violent, or heroic death might be popularly declared a saint locally. The twelfth-century scholar monk Guibert of Nogent reported the case of a young boy who, purely because he died on Easter day, was considered a saint by locals, who even erected a tomb for him and claimed miracles happened there. Another man—“St. Pyro”— fell down a well dead drunk and was deemed a saint. Radegonde of Wellenberg was a young girl known for her charity to the poor. When she got eaten by wolves on her way to visit lepers, she was declared a saint locally. I could multiply examples. Most famously—notoriously?—would be St. Guinefort, a greyhound venerated by locals near Lyon after his master wrongfully killed him.

But more germane to your question, living people could be considered shoo-ins to be saints. Francis of Assisi and Marie d’Oignies were both regarded as living saints. People rushed to touch Francis’ garments to be healed, for example. Even Joan of Arc seems to have been considered a saint. People wanted to touch their rings to hers to gain favor. Some women asked her to come pray for a dead baby who, once she prayed, seemed to momentarily come back to life long enough to be baptized. Few of these local saints ever passed muster of Rome, which codified procedures for canonizing saints in 1234 and by the fourteenth century was very zealous in investigating claims of sainthood.

Check out Andre Vauchez’s Sainthood in the Later Middle Ages for more details.